Using counting arguments, we show that every smallest counterexample to Tutte’s 5-flow Conjecture (that every bridgeless graph has a nowhere-zero 5-flow) has girth at least 9.
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* This work was supported by Science and Technology Assistance Agency under the contract No. APVT-51-027604 and partially by VEGA grant 2/4004/04. The author was also affiliated at the School of Mathematics, Georgia Institute of Technology, the Department of Mathematics, Vanderbilt University.
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Kochol*, M. Restrictions On Smallest Counterexamples To The 5-Flow Conjecture. Combinatorica 26, 83–89 (2006). https://doi.org/10.1007/s00493-006-0006-1
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DOI: https://doi.org/10.1007/s00493-006-0006-1